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Soviet Journal of Quantum Electronics

Quality of image conversion by a quasidegenerate four-photon interaction with tilting

Valery V. Ivakhnik, G. E. Nekrasova

Published Jan 31, 1989• 0 citations
Publisher

Abstract

The form of the spread function of a point is found for a quasidegenerate four-photon parametric interaction of the ω 1 + ω 2 – ω 1 →ω 2 type in a system with tilted pump waves. It is shown that the existence of two phase-matching directions due to a tilt of the pump waves results in doubling of the converted image of a point. When the image plane does not coincide with the optimal focusing plane, there is a critical angle of tilt of the pump waves which ensures the maximum resolution of a parametric radiation converter in the image plane. Allowance for the aperture of the pump waves alters the ratio of the maximum values of the amplitudes of the components of a doubled image of a point.

DOI
10.1070/qe1989v019n01abeh007711

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The form of the spread function of a point is found for a quasidegenerate four-photon parametric interaction of the ω 1 + ω 2 – ω 1 →ω 2 type in a system with tilted pump waves. It is shown that the existence of two phase-matching directions due to a tilt of the pump waves results in doubling of the converted image of a point. When the image plane does not coincide with the optimal focusing plane, there is a critical angle of tilt of the pump waves which ensures the maximum resolution of a parametric radiation converter in the image plane. Allowance for the aperture of the pump waves alters the ratio of the maximum values of the amplitudes of the components of a doubled image of a point.
Quality of the wavefront reversal by a four-wave radiation converter in a parabolic waveguide with resonant nonlinearity have been analyzed using the point spread function. Medium with resonant nonlinearity have been modeled by an ensemble of particles described by a two-level energy scheme. It has been shown that over time, the half-width of the point spread function module decreases, reaching a stationary value, the magnitude of which is determined by the first pump wave intensity in the case of a long waveguide. A decrease in the pump radius at low intensity of the first pump wave leads to a decrease in the half-width of the point spread function modulus (the quality of the wavefront reversal improves), and at high intensity leads to an increase in the half-width of the point spread function modulus (the quality of the wavefront reversal deteriorates) in the stationary case with distribution on the back waveguide face depending on the transverse coordinate of the second pump wave amplitude of the according to the Gaussian law.
Quantum properties of parametric amplification and frequency conversion of an optical image in coupled parametric interactions are analyzed for the case of a remote object. The coupled-wave interaction consists of a traditional process of parametric amplification in the high-frequency pump field accompanied by the frequency mixing of generated and pump waves. The photon number density and signal-to-noise ratio at the interacting frequencies are studied in the image plane at the output of the nonlinear frequency converter in the fixed pump field approximation. The degree of entanglement of optical images at frequencies above and below the pump frequency is investigated.
Abstract In the four‐wave parametric upconverter based on isotropic alkali‐metal vapor which is considered useful as an infrared detector, the acceptance angle characteristics of the infrared ray have been studied theoretically in the case of angle phase matching (or pump phase matching) in which a phase matching is taken by way of small angular difference of two pumping light beams. It is found that various acceptance angle characteristics such as single‐peak, double‐peak, and multi‐peak characteristics can be obtained by adjustment of two pumping light angles, if the collinear phase mismatch is negative due to anomalous dispersion of the metal vapor. The collinear phase mismatch is defined as the magnitude of wave vector of the sum frequency minus the sum of the magnitudes of the wave vectors of two pumping beams and the infrared beam. A flat and broad acceptance angle is obtained in the case of tangential phase matching. It is also found that an optimum state as an image upconverter with a high conversion efficiency and a large acceptance angle exists in the four‐wave parametric upconverter of the two‐photon resonance excitation type in which a large conversion efficiency has been expected.
An investigation was made of the quality of reconstruction of the signal wavefront in a single-pass system for compensation of phase distortions accompanied by frequency up-conversion. It was found that the best resolution and contrast were achieved when the reconstructed field was observed in the optimal focusing plane and the image of an inhomogeneous medium was transferred to the center of a nonlinear converter. The efficiency of the parametric process was enhanced by two-photon excitation of the 3 s –4 s transition in sodium vapor. The converter resolution was 13 lines/mm. The dependence of the contrast in the reconstructed field on the parameters of the compensation system was determined.
Spatial and temporal characteristics of a degenerate four-wave converter in a multimode waveguide with resonant nonlinearity in a scheme with counter-pumping waves are analyzed using the time response function and the point spread function. For single-mode pump waves with equal mode numbers, the dependences of the time response width on the waveguide length, the intensity of the first pump waves, and the mode number in the mode expansion of the object wave amplitude are obtained for the four-wave converter. The greatest contribution to the object wave amplitude is shown to be from the waveguide mode whose number coincides with the mode number of single-mode pump waves. For the stationary model, taking into account the spatial structure of the Gaussian pump wave leads to a monotonous decrease with a decrease in the pump beam width, followed by a constant value of the PSF module width. With single-mode pump waves with equal mode numbers, An increase in the mode number of the pump waves leads to a redistribution of energy concentrated in the side maxima of the point signal image and improvement in the quality of the wavefront reversal for a model with single-mode pump waves with equal mode numbers.